Sometimes I despair for my own gender

Today, at the office, I sat on the sidelines of the following conversation:

Julia: I was at my son's leaver's assembly yesterday and all the kids in his class had to stand up and say what they'd enjoyed most about being in school and what they hoped to do in the future. My son said "I enjoyed the outdoor pursuits weekend and in future I'm going to sail around the world and drive a truck for Eddie Stobart.

[General 'aw' noises] 

Julia: Yeah, and every single girl in my son's class wants to be a vet. All of them said "I love animals, so I want to be a vet." Oh, apart from his one special friend, who's a right tomboy, who said she wants to be a firefighter. A firefighter! She's such a tomboy! I can totally see her as a firefighter.

Me: Good luck to her. I hope she makes it. I always like seeing girls who aren't put off doing what they want to do by the fact it's a traditionally male-dominated area. Our local tyre garage is staffed entirely by women.

Katie: Yeah, but aren't you worried that, like, they won't be as good as when men do it?

Julia: Yeah, I know what you mean. I always have a bit of a panic when you're on a plane and the pilot does the announcement and it's a woman. I mean, I'm always confident if it's a man but a woman? I'm not so sure.

Katie: Though I think I'd trust the women in the tyre garage not to rip me off. I mean, women're more worried about other people's feelings while men? Well they just don't care do they? If they see a woman coming along, especially cos we don't know what we're talking about, and they can just totally think they can take advantage, don't they?

Me: *gapes with disbelief*

I don't quite know what to do with this. I mean, how does one go about challenging that degree of deeply ingrained gender essentialism in women who are in their late twenties and thirties? Some women seem to believe that men are the enemies of feminism and equality but you know what? If we as women buy into the hegemonic discourse about what females can and can't do without even a hint of scepticism, what hope for future generations? Are we to forever to consign ourselves to the gutter by repeating age-old myths of gender-specific capability without question and pass them on to our daughters and granddaughters?